# How can a neural network work with continuous time?

I have an ANN model that receives an input and produces an output. The output is an action that interacts with the environment and changes the input accordingly. The network has a desired environment state which, in any turn, decides the desired response and trains the network on that basis.

Currently, the network works in discrete time. How can I make this network work in a continuous manner? Can you provide some resources and links if there is any past or current research on continuous AI?

To be more concrete, the system starts with the current environment state, for example, [1 1 1], then produces an output. In current system, the next step takes the final state of the system as input, for example, [1 2 2], but we know that such a thing doesn't happen in physical world and the system goes from [1 1 1] to, for example, [1 1 2], and then to [1 2 2], and that middle step is something that a discrete-time AI can't figure out.

The very case that I'm working on is the simulation for an autopilot cart in which the model is incapable to take subtle things like "the maximum speed that you can turn the steering wheel" into consideration. I don't want to add these complexities to the model since if the model is perfect, then the result is deterministic and there is no need for AI. I want the AI to be able to make a decision in each step based on the current state of the system in continuous time.

I don't think the transformation of [1 1 1] into [1 2 2] needs a middle step. Actuators can work simultaneously and they do not have to wait for each other to complete their job. I must even note that, if your next output is [1 2 2], then performing [1 1 2] is so wrong in the case of following a trajectory (if it's your case). So, I guess the middle step in your example is [1 1.5 1.5]. Think of a line segmentation. When you segment a line, you still have your slope, and you do not create "steps". So what you are following in your neural network-based controller is exactly the pattern you need. Your problem is probably the closed-loop frequency of your controller. Better NN performance leads to quicker response and then better actuation.